1 Answer
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I dont think you will solve this easily. The menu plugin you are using is no longer in development (not built with latest jquery in mind), I cant find any info about what browsers it is supposed to work on, and quite frankly it doesn't look that hard to replicate

Your options look like this to me.

1) Spend time trying to work out what the bug is in chrome and fix it (I'm sorry I can't be more help with this).

2) Put together a similar effect in a few lines of your own jquery.

3) Use one of the thousands of similar plugins that do work in all major browsers

4) Look for autocomplete that works with jquery 1.4.2

5) Load both versions of jquery as suggested in comments (I hate this approach - jquery is enough of an overhead without loading it twice)